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st: Cumulative probabilities


From   Evans Jadotte <evans.jadotte@uab.es>
To   statalist@hsphsun2.harvard.edu
Subject   st: Cumulative probabilities
Date   Tue, 20 Oct 2009 16:56:31 +0200

Hello listers,

This is not a Stata question but I hope somebody can give me a hint on this statistical issue.

I am estimating cumulative probabilities of the following function:

y/ijk/ = b0 +b1/x//ijk/ + e/ijk/ + u/.jk/ + u../k

/

where u/.jk/ and u../k /are two random intercepts with variance Sigma^2 (u/.jk/) and Sigma^2 (u/..k/). The variance of my raw residuals is Sigma^2 (e/ijk/)//). The cumulative probabilities I want to calculate are of the form:

Phi((z-xb-uhat/.jk/ - uhat../k/)/sqrt(?))

where Phi denotes the standard normal cumulative density. My question is: should the square root, sqrt, in the denominator contain just the variance of the raw residuals, i.e. Sigma^2 (e/ijk/)//, as some books suggest? Or should it bear, according to my logic, the total variance of the model, which would be the sum Sigma(e^2 /ijk/) + Sigma^2 (u/.jk/) + Sigma^2 (u/..k/)?

Thanks in advance,

Evans

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